According to Bohr's theory the angular momentum of an electron in 5th orbit is :

Options

A. `(10h)/pi`
B. `(25h)/pi`
C. `(1.5h)/pi`
D. `(2.5h)/pi`

Explanation

To find the angular momentum of an electron in the 5th orbit according to Bohr's theory, we can follow these steps:

### Step 1: Understand the formula for angular momentum
According to Bohr's theory, the angular momentum (L) of an electron in a given orbit is given by the formula:
\[ L = \frac{n h}{2 \pi} \]
where:
- \( L \) is the angular momentum,
- \( n \) is the principal quantum number (the orbit number),
- \( h \) is Planck's constant.

### Step 2: Identify the value of \( n \)
In this question, we are asked about the 5th orbit, so we have:
\[ n = 5 \]

### Step 3: Substitute the value of \( n \) into the formula
Now we can substitute \( n \) into the formula for angular momentum:
\[ L = \frac{5 h}{2 \pi} \]

### Step 4: Simplify the expression
To simplify the expression, we can write it as:
\[ L = \frac{5}{2 \pi} h \]
This can also be expressed as:
\[ L = 2.5 \frac{h}{\pi} \]

### Step 5: Conclusion
Thus, the angular momentum of an electron in the 5th orbit according to Bohr's theory is:
\[ L = \frac{5h}{2\pi} \]

### Final Answer
The angular momentum of an electron in the 5th orbit is \( \frac{5h}{2\pi} \).

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